English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The use of spectral projection based methods for simulation of a stochasticsystem with discontinuous solution exhibits the Gibbs phenomenon, which ischaracterized by oscillations near discontinuities. This paper investigates adynamic bi-orthogonality based approach with appropriate post-processing formitigating the effects of the Gibbs phenomenon. The proposed approach usesspectral decomposition of the spatial and stochastic fields in appropriateorthogonal bases, while the dynamic orthogonality condition is used to derivethe resultant closed form evolution equations. The orthogonal decomposition ofthe spatial field is exploited to propose a Gegenbauer reprojection basedpost-processing approach, where the orthogonal bases in spatial dimension arereprojected on the Gegenbauer polynomials in the domain of analyticity. Theresultant spectral expansion in Gegenbauer series is shown to mitigate theGibbs phenomenon. Efficacy of the proposed method is demonstrated forsimulation of a one-dimensional stochastic Burgers equation with uncertaininitial condition.

A Dynamic Bi-orthogonality based Approach for Uncertainty Quantification of Stochastic Systems with Discontinuities